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Saturday, December 4, 2010

Discounted Cash Flows

The benefit measurement methods involve a variety of cash flow analysis techniques including discounted cash flows. Money received in the future is worth less than money received today. The reason for that is the time value of money.

If I borrowed $2,000 from you today and promised to pay it back in three years, you would expect me to pay interest in addition to the original amount borrowed. If you were a family member or a really close friend, maybe you wouldn’t, but ordinarily this is the way it works. You would have had the use of the $2,000 had you not lent it to me. If you had invested the money (does this bring back memories of your mom telling you to save your money?), you’d receive a return on it. Therefore, the future value of the $2,000 you lent me today is $2,315.25 in three years from now at 5 percent interest per year. Here’s the formula for future value calculations:

FV = PV(1 + i)n

In English, this formula says the future value (FV) of the investment equals the present value (PV) times (1 plus the interest rate) raised to the value of the number of time periods (n) the interest is paid. Let’s plug in the numbers:

FV = 2,000(1.05)3

FV = 2,000(1.157625)

FV = $2,315.25

The discounted cash flow technique compares the value of the future cash flows of the project to today’s dollars. In order to calculate discounted cash flows, you need to know the value of the investment in today’s terms, or the PV. PV is calculated as follows:

PV = FV / (1 + i)n

This is the reverse of the FV formula talked about earlier. So, if you ask the question, “What is $2,315.25 in three years from now worth today given a 5 percent interest rate?” you’d use the preceding formula. Let’s try it:

PV = $2,315.25 / (1 + .05)3

PV = $2,315.25 / 1.157625

PV = $2,000$2,315.25 in three years from now is worth $2,000 today.

Discounted cash flow is calculated just like this for the projects you’re comparing for selection purposes or when considering alternative ways of doing the project. Apply the PV formula to the projects you’re considering, and then compare the discounted cash flows of all the projects against each other to make a selection. Here is an example comparison of two projects using this technique:

Project A is expected to make $100,000 in two years.

Project B is expected to make $120,000 in three years.

If the cost of capital is 12 percent, which project should you choose?

Using the PV formula used previously, calculate each project’s worth:

The PV of Project A = $79,719.

The PV of Project B = $85,414.

Project B is the project that will return the highest investment to the company and should be chosen over Project A.